Question

1. Suppose 100 individual aged 25 purchase $1000 of whole life insurance with benefits payable at death. If Z, is the present value of benefit variable for the ith individual, then Zag Z1Z2 +. Z100 is the aggregate random present value of benefits paid by the insurer. Write an expression for the expected value and variance of Zagg in terms of A25 and 2 A25

A25=E( $Z_{x}$ )

It is a life insurance models question.

Answer 1

This is a simple actuarial problem. I am going to be using the standard notations to solve the same.

in by Nuw 一-) () dt 2. 2.5 2 S

Naw 49 E(2) E()E (210) 1000 Aus+ lo00 As+ +1000 A 25 て /d0OX loo A2S 100000A2s 100, 000 2 - loo X Via (1000 2x) loo x (0o0) vis (7,) (10000) Vs ( Zx) -(1o0uo)

ence Va C2(1o, 000) G4